Electronic configuration and control for acoustic standing wave generation

ABSTRACT

Aspects of the disclosure are directed to an apparatus for separating a second fluid or a particulate from a host fluid. That apparatus comprises a flow chamber with at least one inlet and at least one outlet. A drive circuit configured to provide a drive signal to a filter circuit configured to receive the drive signal and provide a translated drive signal. An ultrasonic transducer is cooperatively arranged with the flow chamber, and transducer includes at least one piezoelectric element configured to be driven by the current drive signal to create an acoustic standing wave in the flow chamber. At least one reflector opposing the ultrasonic transducer to reflect acoustic energy.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/960,451 filed Apr. 23, 2018, which is a continuation of U.S. patentapplication Ser. No. 15/495,471 filed Apr. 24, 2017, now U.S. Pat. No.9,950,282, which claims the benefit of U.S. Provisional PatentApplication Ser. No. 62/461,691 filed Feb. 21, 2017, U.S. ProvisionalPatent Application Ser. No. 62/446,356 filed Jan. 13, 2017, and U.S.Provisional Patent Application Ser. No. 62/326,766 filed Apr. 24, 2016.U.S. patent application Ser. No. 15/495,471 is also acontinuation-in-part of U.S. patent application Ser. No. 15/371,037filed Dec. 6, 2016, which is a continuation of U.S. patent applicationSer. No. 14/533,753 filed Nov. 5, 2014, now U.S. Pat. No. 9,512,395which claims the benefit of U.S. Provisional Patent Application Ser. No.62/020,088 filed Jul. 2, 2014 and U.S. Provisional Patent ApplicationSer. No. 61/900,395 filed Nov. 5, 2013. U.S. patent application Ser. No.15/495,471 is also a continuation-in-part of U.S. patent applicationSer. No. 15/285,349 filed Oct. 4, 2016, which is a continuation-in-partof U.S. patent application Ser. No. 14/708,035 filed May 8, 2015, nowU.S. Pat. No. 9,457,302, which claims priority to U.S. ProvisionalPatent Application Ser. No. 61/990,168 filed May 8, 2014, and is also acontinuation-in-part of U.S. patent application Ser. No. 14/026,413filed Sep. 13, 2013, now U.S. Pat. No. 9,458,450, which is acontinuation-in-part of U.S. patent application Ser. No. 13/844,754filed Mar. 15, 2013, now U.S. Pat. No. 10,040,011, which claims priorityto U.S. Provisional Patent Application Ser. No. 61/754,792 filed Jan.21, 2013, U.S. Provisional Patent Application Ser. No. 61/708,641 filedOct. 2, 2012, U.S. Provisional Patent Application Ser. No. 61/611,240filed Mar. 15, 2012 and U.S. Provisional Patent Application Ser. No.61/611,159 filed Mar. 15, 2012. U.S. patent application Ser. No.15/495,471 is also a continuation-in-part of U.S. patent applicationSer. No. 15/284,529 filed Oct. 3, 2016, now U.S. Pat. No. 9,796,956,which claims priority to U.S. Provisional Application Ser. No.62/322,262 filed Apr. 14, 2016, U.S. Provisional Application Ser. No.62/307,489 filed Mar. 12, 2016, and U.S. Provisional Application Ser.No. 62/235,614 filed Oct. 1, 2015. All of the above disclosures areincorporated herein by reference in their entireties.

BACKGROUND

Acoustophoresis is the separation of particles and secondary fluids froma primary or host fluid using acoustics, such as acoustic standingwaves. Acoustic standing waves can exert forces on particles in a fluidwhen there is a differential in density and/or compressibility,otherwise known as the acoustic contrast factor. The pressure profile ina standing wave contains areas of local minimum pressure amplitudes atstanding wave nodes and local maxima at standing wave anti-nodes.Depending on their density and compressibility, the particles can betrapped at the nodes or anti-nodes of the standing wave. Generally, thehigher the frequency of the standing wave, the smaller the particlesthat can be trapped.

At a micro scale, for example with structure dimensions on the order ofmicrometers, conventional acoustophoresis systems tend to use half orquarter wavelength acoustic chambers, which at frequencies of a fewmegahertz are typically less than a millimeter in thickness, and operateat very slow flow rates (e.g., μL/min). Such systems are not scalablesince they benefit from extremely low Reynolds number, laminar flowoperation, and minimal fluid dynamic optimization.

At the macro-scale, planar acoustic standing waves have been used inseparation processes. However, a single planar wave tends to trap theparticles or secondary fluid such that separation from the primary fluidis achieved by turning off or removing the planar standing wave. Theremoval of the planar standing wave may hinder continuous operation.Also, the amount of power that is used to generate the acoustic planarstanding wave tends to heat the primary fluid through waste energy,which may be disadvantageous for the material being processed.

Conventional acoustophoresis devices have thus had limited efficacy dueto several factors including heat generation, use of planar standingwaves, limits on fluid flow, and the inability to capture differenttypes of materials.

Control of power supplied to an ultrasonic transducer is challenging toimplement, and in particular is challenging to implement with efficientperformance. Promoting multimode behavior in a resonance-cavity systemmay depend on providing sufficient electrical power to an ultrasonictransducer in the system.

BRIEF SUMMARY

The following presents a simplified summary in order to provide a basicunderstanding of some aspects of the disclosure. The summary is not anextensive overview of the disclosure. It is neither intended to identifykey or critical elements of the disclosure nor to delineate the scope ofthe disclosure. The following summary merely presents some concepts ofthe disclosure in a simplified form as a prelude to the descriptionbelow.

Examples of the disclosure are directed to an apparatus for separating asecond fluid or a particulate from a host fluid, comprising a flowchamber having opposing first and second walls, at least one inlet andat least one outlet. A control circuit provides a drive signal and ascaling circuit receives the drive signal and provides an equivalentcurrent source drive signal, where the scaling circuit providesimpedance and source translation with respect to the ultrasonictransducer. An ultrasonic transducer, having a transducer inputimpedance and located within the flow chamber includes at least onepiezoelectric element driven by the equivalent current source drivesignal to create an acoustic standing wave in the flow chamber. At leastone reflector is located on the first wall on the opposite side of theflow chamber from the at least one ultrasonic transducer.

The control circuit may comprise a voltage source.

The acoustic standing wave may comprise a multi-dimensional acousticstanding wave. The multi-dimensional acoustic standing wave may begenerated from a single piezoelectric element or a plurality ofpiezoelectric elements, perturbed in a higher order mode.

The scaling circuit may comprise an inductor that includes a firstterminal and a second terminal, and a capacitor that includes a thirdterminal and a fourth terminal, where the first terminal receives thedrive signal, the second and third terminals are connected, the fourthterminal is connected to a reference potential, and a signal indicativeof the equivalent current source drive signal is provided at the secondand third terminals.

The scaling circuit may consist of passive circuit components.

Aspects of the disclosure are also directed to an apparatus forseparating a secondary fluid or particulates from a host fluid,comprising a flow chamber having opposing first and second walls, atleast one inlet and at least one outlet. A circuit is configured toreceive a drive signal and provides a translated drive signal. Anultrasonic transducer is located within the flow chamber, the transducerincludes at least one piezoelectric element that receive the translateddrive signal to create an acoustic standing wave in the flow chamber. Atleast one reflector is located on the wall on the opposite side of theflow chamber from the at least one ultrasonic transducer.

The acoustic standing wave may include a multi-dimensional acousticstanding wave.

The circuit may comprise a scaling circuit that receives the drivesignal and provides the translated drive signal, where the scalingcircuit provides impedance and source translation with respect to theultrasonic transducer.

The scaling circuit may comprise a first inductor, a first capacitor anda second inductor cooperatively arranged as a low pass filter.

The scaling circuit may comprise an inductor that includes a firstterminal and a second terminal, and a capacitor that includes a thirdterminal and a fourth terminal, where the first terminal receives thedrive signal, the second and third terminals are connected, the fourthterminal is connected to a reference potential, and a signal indicativeof the equivalent translated drive signal is provided at the second andthird terminals.

The scaling circuit may consist of passive circuit components.

A first tap may sense voltage across the ultrasonic transducer. Thetransducer may be composed of or include piezoelectric material, whichmay be implemented as a ceramic crystal, a poly-crystal or othercrystal, all of which may collectively be referred to herein as acrystal. The first tap may provide a sensed voltage signal indicative ofa voltage across the transducer, and a current sensing coil may sensecurrent and provide a sensed current signal indicative of crystalcurrent.

A controller may receive and process the sensed current signal and thesensed voltage signal to control the drive signal.

The circuit may comprise a first inductor that includes a first terminaland a second terminal, a first capacitor that includes a third terminaland a fourth terminal, and a second inductor that includes a fifthterminal and sixth terminal, there the first terminal receives a signalindicative of the drive signal, the second terminal is connected to thethird terminal and the fifth terminal, the fourth terminal is connectedto a reference voltage, and an output signal indicative of the currentdrive signal is provided on the sixth terminal.

Aspects of the disclosure are further directed to an apparatus forseparating a second fluid or a particulate from a host fluid, comprisinga flow chamber having opposing first and second walls, and at least oneinlet and at least one outlet. A drive circuit is configured to providea drive signal, and a filter circuit is configured to receive the drivesignal and provide a translated drive signal. An ultrasonic transduceris cooperatively arranged with the flow chamber, the transducerincluding one or more at least one piezoelectric element driven by thecurrent drive signal to create an acoustic standing wave in the flowchamber. At least one reflector is located on the second wall opposingthe ultrasonic transducer to receive the acoustic standing waves.

The acoustic standing wave may comprise a multi-dimensional acousticstanding wave.

The filter circuit may comprise an inductor that includes a firstterminal and a second terminal, and a capacitor that includes a thirdterminal and a fourth terminal, where the first terminal receives thedrive signal, the second and third terminals are connected, the fourthterminal is connected to a reference potential, and a signal indicativeof the equivalent current source drive signal is provided at the secondand third terminals.

The filter circuit may comprise a first inductor that includes a firstterminal and a second terminal, a first capacitor that includes a thirdterminal and a fourth terminal, and a second inductor that includes afifth terminal and sixth terminal, there the first terminal receives asignal indicative of the drive signal, the second terminal is connectedto the third terminal and the fifth terminal, the fourth terminal isconnected to a reference voltage, and an output signal indicative of thecurrent drive signal is provided on the sixth terminal.

The filter may consist of passive circuit components.

The voltage drive signal may be substantially a square wave, and thetranslated signal may be substantially a sine wave.

BRIEF DESCRIPTION OF THE DRAWINGS

The following is a brief description of the drawings, which arepresented for the purposes of illustrating the exemplary embodimentsdisclosed herein and not for the purposes of limiting the same.

FIG. 1A is a diagram illustrating the function of an acoustophoreticseparator with a secondary fluid or particles less dense than the hostfluid.

FIG. 1B is a diagram illustrating the function of an acoustophoreticseparator with a secondary fluid or particles denser than the hostfluid.

FIG. 2 is a cross-sectional diagram of a conventional ultrasonictransducer.

FIG. 3A is a cross-sectional diagram of an ultrasonic transducerstructure that can be used in the present disclosure. An air gap ispresent within the transducer, and no backing layer or wear plate ispresent.

FIG. 3B is a cross-sectional diagram of an ultrasonic transducerstructure that can be used in the present disclosure. An air gap ispresent within the transducer, and a backing layer and wear plate arepresent.

FIG. 4 is a conventional single-piece monolithic piezoelectric crystalused in an ultrasonic transducer.

FIG. 5 is an exemplary rectangular piezoelectric array having 16piezoelectric elements used in the transducers of the presentdisclosure.

FIG. 6 is another exemplary rectangular piezoelectric array having 25piezoelectric elements used in the transducers of the presentdisclosure.

FIG. 7 is a graph showing the relationship of the acoustic radiationforce, gravity/buoyancy force, and Stokes' drag force to particle size.The horizontal axis is in microns (μm) and the vertical axis is inNewtons (N).

FIG. 8 is a graph of electrical impedance amplitude versus frequency fora square transducer driven at different frequencies.

FIG. 9A illustrates the trapping line configurations for seven of theminima amplitudes of FIG. 8 from the direction orthogonal to fluid flow.

FIG. 9B is a perspective view illustrating the separator. The fluid flowdirection and the trapping lines are shown.

FIG. 9C is a view from the fluid inlet along the fluid flow direction(arrow 114) of FIG. 9B, showing the trapping nodes of the standing wavewhere particles would be captured.

FIG. 9D is a view taken through the transducers face at the trappingline configurations, along arrow 116 as shown in FIG. 9B.

FIG. 10A shows an acoustophoretic separator for separating buoyantmaterials.

FIG. 10B is a magnified view of fluid flow near the intersection of thecontoured nozzle wall 129 and the collection duct 137.

FIG. 11A shows an exploded view of an acoustophoretic separator used inBio-Pharma applications.

FIG. 11B shows an exploded view of a stacked acoustophoretic separatorwith two acoustic chambers.

FIG. 12A is a graph showing the efficiency of removing cells from amedium using a Beckman Coulter Cell Viability Analyzer for oneexperiment.

FIG. 12B is a graph showing the efficiency of removing cells from amedium using a Beckman Coulter Cell Viability Analyzer for anotherexperiment.

FIG. 13 shows a schematic of a two-dimensional numerical model developedfor the simulation of an ultrasonic transducer and transducer array.

FIGS. 14A-14D are diagrams comparing the results of the numerical model(bottom) of FIG. 13 against published data (top), illustrating theaccuracy of the numerical model. FIG. 14A compares the acousticpotential U. FIG. 14B compares the x-component of the acoustic radiationforce (ARF). FIG. 14C compares the y-component of the ARF. FIG. 14Dcompares the absolute value of the ARF.

FIG. 15 is a diagram showing the amplitude of the acoustic standing wavegenerated by a monolithic piezoelectric crystal in the model of FIG. 13.The frequency is at 2.245 MHz. The horizontal axis is the location alongthe X-axis, and the vertical axis is the location along the Y-axisbetween the transducer and the reflector.

FIG. 16 is a diagram showing the amplitude of the acoustic standing wavegenerated by the 4-element piezoelectric array in the model of FIG. 13.The frequency is at 2.245 MHz with phasing between the elements beingvaried.

FIG. 17 is a diagram showing the amplitude of the acoustic standing wavegenerated by the 5-element piezoelectric array in the model of FIG. 13.The frequency is at 2.245 MHz with phasing between the elements beingvaried.

FIG. 18 is a picture of an acoustophoretic setup with a 4×4piezoelectric array made from a 2 MHz PZT-8 crystal with kerfs made inthe crystal, as shown in FIG. 5.

FIG. 19 is a comparison of the simulation of an out-of-phasepiezoelectric array with an actual acoustophoretic experiment using theout-of-phase array. For this simulation, out-of-phase refers to thephase angle of the delivered voltage. For out-of-phase testing, thephasing varied from 0°-180°-0°-180° for the numerical model. For theexperimental test, the elements were varied in a checkerboard pattern.

FIG. 20 is a comparison of the simulation of an in-phase piezoelectricarray with an actual acoustophoretic experiment using the in-phasearray. For this simulation, in-phase refers to the phase angle of thedelivered voltage. For in-phase testing, the phasing was kept constantbetween all elements.

FIG. 21 is a picture illustrating a kerfed crystal (top) versus atransducer array that has piezoelectric elements joined together by apotting material (bottom).

FIG. 22 is a diagram showing the out-of-phase modes tested for the4-element array.

FIG. 23 is a diagram showing the out-of-phase modes tested for the5-element array.

FIG. 24 is a graph showing the normalized acoustic radiation force (ARF)from a monolithic piezoelectric crystal simulation.

FIG. 25 is a graph showing the ratio of the ARF components (lateral toaxial) for a monolithic piezoelectric crystal simulation.

FIG. 26 is a graph showing the normalized acoustic radiation force (ARF)for a 5-element simulation with varying phasing.

FIG. 27 is a graph showing the ratio of the ARF components (lateral toaxial) for the 5-element simulation.

FIG. 28 is a diagram showing the phasing of the arrays duringout-of-phase testing. Dark elements had a 0° phase angle and lightelement had a 180° phase angle when tested.

FIG. 29 is a circuit diagram of an RF power supply with an LCL networkthat provides a transducer drive signal to an ultrasonic transducer.

FIG. 30 is a graph illustrating a frequency response for an LC network.

FIG. 31 is a circuit diagram of a buck low pass filter used with the RFpower supply of FIG. 29.

FIG. 32 is a block diagram illustration of a system for providing thetransducer drive signal to the transducer.

FIG. 33 is a graph illustrating a frequency response for an acoustictransducer.

FIG. 34 is a block diagram illustration of an alternative embodimentsystem for providing the transducer drive signal to the transducer.

FIG. 35 is a block diagram illustrating a calculation technique forobtaining control parameters for an acoustic transducer.

FIG. 36 is a block diagram illustrating demodulation of a voltage orcurrent signal.

FIG. 37 is a simplified illustration of an RF power supply including anLC filter that provides the transducer drive signal.

FIG. 38 is a simplified illustration of an alternative RF power supplyincluding an LCL filter that provides the transducer drive signal.

FIG. 39 is a circuit diagram of an RF power supply that provides a drivesignal to an LCL filter that provides a transducer drive signal to anultrasonic transducer.

FIG. 40 is a circuit illustration of an LCL filter circuit with a tapthat provides a current sense signal and a node that provides a voltagesense signal that can be fed back to a controller (e.g., a DSP) tocontrol the drive signal delivered to the transducer.

FIG. 41 is a schematic illustration of an embodiment of a power supplywith an LCL filter network that provides a transducer drive signal.

DETAILED DESCRIPTION

The present disclosure may be understood more readily by reference tothe following detailed description of desired embodiments and theexamples included therein. In the following specification and the claimswhich follow, reference will be made to a number of terms which shall bedefined to have the following meanings.

The singular forms “a,” “an,” and “the” include plural referents unlessthe context clearly dictates otherwise.

The term “comprising” is used herein as requiring the presence of thenamed components/steps and allowing the presence of othercomponents/steps. The term “comprising” should be construed to includethe term “consisting of”, which allows the presence of only the namedcomponents/steps, along with any impurities that might result from themanufacture of the named components/steps.

Numerical values should be understood to include numerical values whichare the same when reduced to the same number of significant figures andnumerical values which differ from the stated value by less than theexperimental error of conventional measurement technique of the typedescribed in the present application to determine the value.

All ranges disclosed herein are inclusive of the recited endpoint andindependently combinable (for example, the range of “from 2 grams to 10grams” is inclusive of the endpoints, 2 grams and 10 grams, and all theintermediate values).

The terms “substantially” and “about” can be used to include anynumerical value that can vary without changing the basic function ofthat value. When used with a range, “substantially” and “about” alsodisclose the range defined by the absolute values of the two endpoints,e.g. “about 2 to about 4” also discloses the range “from 2 to 4.” Theterms “substantially” and “about” may refer to plus or minus 10% of theindicated number.

It should be noted that many of the terms used herein are relativeterms. For example, the terms “upper” and “lower” are relative to eachother in location, i.e. an upper component is located at a higherelevation than a lower component in a given orientation, but these termscan change if the device is flipped. The terms “inlet” and “outlet” arerelative to a fluid flowing through them with respect to a givenstructure, e.g. a fluid flows through the inlet into the structure andflows through the outlet out of the structure. The terms “upstream” and“downstream” are relative to the direction in which a fluid flowsthrough various components, i.e. the flow fluids through an upstreamcomponent prior to flowing through the downstream component. It shouldbe noted that in a loop, a first component can be described as beingboth upstream of and downstream of a second component.

The terms “horizontal” and “vertical” are used to indicate directionrelative to an absolute reference, i.e. ground level. The terms “above”and “below”, or “upwards” and “downwards” are also relative to anabsolute reference; an upwards flow is always against the gravity of theearth.

The present application refers to “the same order of magnitude.” Twonumbers are of the same order of magnitude if the quotient of the largernumber divided by the smaller number is a value less than 10.

The acoustophoretic separation technology of the present disclosureemploys ultrasonic acoustic standing waves to trap, i.e., holdstationary, particles or a secondary fluid in a host fluid stream. Theparticles or secondary fluid collect at the nodes or anti-nodes of themulti-dimensional acoustic standing wave, depending on the particles' orsecondary fluid's acoustic contrast factor relative to the host fluid,forming clusters that eventually fall out of the multi-dimensionalacoustic standing wave when the clusters have grown to a size largeenough to overcome the holding force of the multi-dimensional acousticstanding wave (e.g. by coalescence or agglomeration). The scattering ofthe acoustic field off the particles results in a three-dimensionalacoustic radiation force, which acts as a three-dimensional trappingfield. The acoustic radiation force is proportional to the particlevolume (e.g. the cube of the radius) when the particle is small relativeto the wavelength. It is proportional to frequency and the acousticcontrast factor. It also scales with acoustic energy (e.g. the square ofthe acoustic pressure amplitude). For harmonic excitation, thesinusoidal spatial variation of the force is what drives the particlesto the stable axial positions within the standing waves. When theacoustic radiation force exerted on the particles is stronger than thecombined effect of fluid drag force and buoyancy and gravitationalforce, the particle is trapped within the acoustic standing wave field.This continuous trapping results in concentration, aggregation,clustering, agglomeration and/or coalescence of the trapped particlesthat will then continuously fall out of the multi-dimensional acousticstanding wave through gravity separation. The strong lateral forcescreate rapid clustering of particles. Relatively large solids of onematerial can thus be separated from smaller particles of a differentmaterial, the same material, and/or the host fluid through enhancedgravitational separation.

In this regard, the contrast factor is the difference between thecompressibility and density of the particles and the fluid itself. Theseproperties are characteristic of the particles and the fluid themselves.Most cell types present a higher density and lower compressibility thanthe medium in which they are suspended, so that the acoustic contrastfactor between the cells and the medium has a positive value. As aresult, the axial acoustic radiation force (ARF) drives the cells, witha positive contrast factor, to the pressure nodal planes, whereas cellsor other particles with a negative contrast factor are driven to thepressure anti-nodal planes. The radial or lateral component of theacoustic radiation force trap the cells. The radial or lateral componentof the ARF is larger than the combined effect of fluid drag force andgravitational force. The radial or lateral component drives thecells/particles to planes where they can cluster into larger groups,which will then gravity separate from the fluid.

As the cells agglomerate at the nodes of the standing wave, there isalso a physical scrubbing of the cell culture media that occurs wherebymore cells are trapped as they come in contact with the cells that arealready held within the standing wave. This effect contributes toseparating the cells from the cell culture media. The expressedbiomolecules remain in the nutrient fluid stream (i.e. cell culturemedium).

For three-dimensional acoustic fields, Gor'kov's formulation can be usedto calculate the acoustic radiation force F_(ac) applicable to any soundfield. The primary acoustic radiation force F_(ac) is defined as afunction of a field potential U,

F _(A)=−∇(U),

where the field potential U is defined as

$U = {V_{0}\left\lbrack {{\frac{\left\langle p^{2} \right\rangle}{2\rho_{f}c_{f}^{2}}f_{1}} - {\frac{3\rho_{f}\left\langle u^{2} \right\rangle}{4}f_{2}}} \right\rbrack}$

and f₁ and f₂ are the monopole and dipole contributions defined by

${f_{1} = {1 - \frac{1}{\Lambda\sigma^{2}}}},{f_{2} = \frac{2\left( {\Lambda - 1} \right)}{{2\Lambda} + 1}},$

where p is the acoustic pressure, u is the fluid particle velocity, Λ isthe ratio of cell density ρ_(p) to fluid density ρ_(f), σ is the ratioof cell sound speed c_(p) to fluid sound speed c_(f), V_(o) is thevolume of the cell, and < > indicates time averaging over the period ofthe wave. Gor'kov's formulation applies to particles smaller than thewavelength. For larger particle sizes, Ilinskii provides equations forcalculating the 3D acoustic radiation forces for any particle size. SeeIlinskii, Acoustic Radiation Force on a Sphere in Tissue, The Journal ofthe Acoustical Society of America, 132, 3, 1954 (2012), which isincorporated herein by reference.

An acoustic transducer can be driven to produce an acoustic wave. Theacoustic wave can be reflected with another acoustic transducer or areflector to generate an acoustic standing wave. Alternately, or inaddition, two opposing acoustic transducers can be driven to generate anacoustic standing wave between them. Perturbation of the piezoelectriccrystal in an ultrasonic transducer in a multimode fashion allows forgeneration of a multidimensional acoustic standing wave. A piezoelectricmaterial or crystal can be specifically designed to deform in amultimode fashion at designed frequencies, allowing for generation of amulti-dimensional acoustic standing wave. The multi-dimensional acousticstanding wave may be generated by distinct modes of the piezoelectricmaterial or crystal such as the 3×3 mode that would generatemultidimensional acoustic standing waves. A multitude ofmultidimensional acoustic standing waves may also be generated byallowing the piezoelectric material or crystal to vibrate through manydifferent mode shapes. Thus, the crystal would excite multiple modessuch as a 0×0 mode (i.e. a piston mode) to a 1×1, 2×2, 1×3, 3×1, 3×3,and other higher order modes and then cycle back through the lower modesof the crystal (not necessarily in straight order). This switching ordithering of the piezoelectric material or crystal between modes allowsfor various multidimensional wave shapes, along with a single pistonmode shape to be generated over a designated time.

In some examples of the present disclosure, a single ultrasonictransducer contains a rectangular array of piezoelectric elements, whichcan be operated such that some components of the array will be out ofphase with other components of the array. This phased-array arrangementcan also separate materials in a fluid stream. A single piezoelectricelement may be used rather than a piezoelectric array.

One specific application for the acoustophoresis device is in theprocessing of bioreactor materials. In a fed batch bioreactor, it isimportant at the end of the production cycle to filter all of the cellsand cell debris from the expressed materials that are in the fluidstream. The expressed materials are composed of biomolecules such asrecombinant proteins or monoclonal antibodies, and are the desiredproduct to be recovered. Through the use of acoustophoresis, theseparation of the cells and cell debris is very efficient and leads tovery little loss of the expressed materials. The use of acoustophoresisis an improvement over the current filtration processes (depthfiltration, tangential flow filtration, centrifugation), which showlimited efficiencies at high cell densities, so that the loss of theexpressed materials in the filter beds themselves can be up to 5% of thematerials produced by the bioreactor. The use of mammalian cell cultureincludes Chinese hamster ovary (CHO), NS0 hybridoma cells, baby hamsterkidney (BHK) cells, and human cells has proven to be a very efficaciousway of producing/expressing the recombinant proteins and monoclonalantibodies used to produce pharmaceuticals. The filtration of themammalian cells and the mammalian cell debris through acoustophoresisaids in greatly increasing the yield of the fed batch bioreactor. Theacoustophoresis process, through the use of multidimensional acousticwaves, may also be coupled with a standard filtration process upstreamor downstream, such as depth filtration using diatomaceous earth,tangential flow filtration (TFF), or other physical filtrationprocesses.

Another type of bioreactor, a perfusion reactor, uses continuousexpression of the target protein or monoclonal antibodies from the CHOcells. The continuous nature of the perfusion reactor enables a muchsmaller footprint in faster production cycle. The use of acoustophoresisto hold the CHO cells in a fluid stream as they are producing/expressingthe proteins is a very efficient and closed loop way of production. Italso allows for an increased or maximum production efficiency of theproteins and monoclonal antibodies in that none of the materials arelost in a filter bed.

In the fed batch bioreactor process, the acoustophoresis device usessingular or multiple standing waves to trap the cells and cell debris.The cells and cell debris, having a positive contrast factor, move tothe nodes (as opposed to the anti-nodes) of the standing wave. As thecells and cell debris agglomerate at the nodes of the standing wave,there is also a physical scrubbing of the fluid stream that occurswhereby more cells are trapped as they come in contact with the cellsthat are already held within the standing wave. When the cells in themulti-dimensional acoustic standing wave agglomerate to the extent wherethe mass is no longer able to be held by the acoustic wave, theaggregated cells and cell debris that have been trapped fall out of thefluid stream through gravity, and can be collected separately. Thiseffect permits cells to be separated in a continuous process ofgravitational separation.

Advanced multi-physics and multiple length scale computer models andhigh frequency (MHz), high-power, and high-efficiency ultrasonic driverswith embedded controls have been combined to arrive at new designs ofacoustic resonators driven by an array of piezoelectric transducers,resulting in acoustophoretic separation devices that far surpass currentcapabilities.

Desirably, such transducers generate a multi-dimensional acousticstanding wave in the fluid that exerts a lateral force on the suspendedparticles/secondary fluid to accompany the axial force so as to increasethe particle trapping capabilities of an acoustophoretic system. Typicalresults published in literature state that the lateral force is twoorders of magnitude smaller than the axial force. In contrast, thetechnology disclosed in this application provides for a lateral force tobe of the same order of magnitude as the axial force.

The system may be driven by a controller and amplifier (not shown). Thesystem performance may be monitored and controlled by the controller.The parameters of the excitation of the transducer may be modulated. Forexample, the frequency, current or voltage of the transducer excitationor drive signal may be modulated to change characteristics of thegenerated acoustic standing wave. The amplitude modulation and/or byfrequency modulation can be controlled by the computer. The duty cycleof the propagation of the standing wave may also be utilized to achievecertain results for trapping of materials. The acoustic standing wavemay be turned on and/or shut off at different frequencies to achievedesired results.

The lateral force of the total acoustic radiation force (ARF) generatedby the ultrasonic transducers of the present disclosure is significantand is sufficient to overcome the fluid drag force at high linearvelocities up to 2 cm/s and beyond. For example, linear velocitiesthrough the devices of the present disclosure can be as small or smallerthan 4 cm/min for separation of cells/particles, and can be as high as 2cm/sec for separation of oil/water phases. Flow rates can be as small orsmaller than 25 mL/min, and can range as high as 40 mL/min to 1000mL/min, or even higher. These flow rates in an acoustophoretic systemare applicable for batch reactors, fed-batch bioreactors and perfusionbioreactors.

A diagrammatic representation of an embodiment for removing oil or otherlighter-than-water material is shown in FIG. 1A. Excitation frequenciestypically in the range from hundreds of kHz to 10s of MHz are applied bytransducer 10. One or more standing waves are created between thetransducer 10 and the reflector 11. Microdroplets or particles 12 aretrapped in standing waves at the pressure anti-nodes 14 where theyagglomerate, aggregate, clump, or coalesce, and, in the case of buoyantmaterial, float to the surface and are discharged via an effluent outlet16 located above the flow path. Clarified fluid is discharged at outlet18. The acoustophoretic separation technology can accomplishmulti-component particle separation without any fouling at amuch-reduced cost.

A diagrammatic representation of an embodiment for removing contaminantsor other heavier-than-water material is shown in FIG. 1B. Excitationfrequencies typically in the range from hundreds of kHz to 10s of MHzare applied by transducer 10. Contaminants in the incoming fluid 13 aretrapped in standing waves at the pressure nodes 15 where theyagglomerate, aggregate, clump, or coalesce, and, in the case of heaviermaterial, sink to the bottom collector and are discharged via aneffluent outlet 17 located below the flow path. Clarified water isdischarged at outlet 18.

Generally, the transducers are arranged so that they cover the entirecross-section of the flow path. The acoustophoretic separation system ofFIG. 1A or FIG. 1B has, in certain embodiments, a square cross sectionof 6.375 inches×6.375 inches which operates at flow rates of up to 5gallons per minute (GPM), or a linear velocity of 12.5 mm/sec. Thetransducers 10 are PZT-8 (Lead Zirconate Titanate) transducers with a 1inch×1 inch square cross section and a nominal 2 or 3 MHz resonancefrequency. Each transducer consumes about 60 W of power for droplettrapping at a flow rate of 5 GPM. This power consumption translates inan energy cost of 0.500 kW hr/m³. This low power usage is an indicationof the very low cost of energy of this technology. Desirably, eachtransducer is powered and controlled by its own amplifier. Oneapplication for this embodiment is to shift the particle sizedistribution through agglomeration, aggregation, clumping or coalescingof the micron-sized oil droplets into much larger droplets.

FIG. 2 is a cross-sectional diagram of a conventional ultrasonictransducer. This transducer has a wear plate 50 at a bottom end, epoxylayer 52, ceramic crystal 54 (made of, e.g. PZT), an epoxy layer 56, anda backing layer 58. On either side of the ceramic crystal, there is anelectrode: a positive electrode 61 and a negative electrode 63. Theepoxy layer 56 attaches backing layer 58 to the crystal 54. The entireassembly is contained in a housing 60 which may be made out of, forexample, aluminum. An electrical adapter 62 provides connection forwires to pass through the housing and connect to leads (not shown) whichattach to the crystal 54. Typically, backing layers are designed to adddamping and to create a broadband transducer with uniform displacementacross a wide range of frequency and are designed to suppress excitationat particular vibrational eigenmodes. Wear plates are usually designedas impedance transformers to better match the characteristic impedanceof the medium into which the transducer radiates.

FIG. 3A is a cross-sectional view of an ultrasonic transducer 81 of thepresent disclosure, which can be used in acoustophoretic separator.Transducer 81 is shaped as a disc or a plate, and has an aluminumhousing 82. The piezoelectric crystal is a mass of perovskite ceramiccrystals, each consisting of a small, tetravalent metal ion, usuallytitanium or zirconium, in a lattice of larger, divalent metal ions,usually lead or barium, and O²⁻ ions. As an example, a PZT (leadzirconate titanate) crystal 86 defines the bottom end of the transducer,and is exposed from the exterior of the housing. The crystal issupported on its perimeter by a small elastic layer 98, e.g. silicone orsimilar material, located between the crystal and the housing. Putanother way, no wear layer is present.

Screws 88 attach an aluminum top plate 82 a of the housing to the body82 b of the housing via threads. The top plate includes a connector 84for powering the transducer. The top surface of the PZT crystal 86 isconnected to a positive electrode 90 and a negative electrode 92, whichare separated by an insulating material 94. The electrodes can be madefrom any conductive material, such as silver or nickel. Electrical poweris provided to the PZT crystal 86 through the electrodes on the crystal.Note that the crystal 86 has no backing layer or epoxy layer as ispresent in FIG. 2. Put another way, there is an air gap 87 in thetransducer between aluminum top plate 82 a and the crystal 86 (i.e. theair gap is completely empty). A relatively minimal backing 58 and/orwear plate 50 may be provided in some embodiments, as seen in FIG. 3B.

The transducer design can affect performance of the system. A typicaltransducer is a layered structure with the ceramic crystal bonded to abacking layer and a wear plate. Because the transducer is loaded withthe high mechanical impedance presented by the fluid, the traditionaldesign guidelines for wear plates, e.g., half wavelength thickness forstanding wave applications or quarter wavelength thickness for radiationapplications, and manufacturing methods may not be appropriate. Rather,in one embodiment of the present disclosure the transducers have no wearplate or backing, allowing the crystal (e.g., a polycrystal,piezoelectric material or a single crystal (i.e., quartz)) to vibrate inone of its eigenmodes with a high Q-factor. The vibrating ceramiccrystal/disk is directly exposed to the fluid flowing through the flowchamber.

Removing the backing (e.g. making the crystal air backed) also permitsthe ceramic crystal to vibrate at higher order modes of vibration withlittle damping (e.g. higher order modal displacement). In a transducerhaving a crystal with a backing, the crystal vibrates with a moreuniform displacement, like a piston. Removing the backing allows thecrystal to vibrate in a non-uniform displacement mode. The higher orderthe mode shape of the crystal, the more nodal lines the crystal has. Thehigher order modal displacement of the crystal creates more trappinglines, although the correlation of trapping line to node is notnecessarily one to one, and driving the crystal at a higher frequencywill not necessarily produce more trapping lines. See the discussionbelow with respect to FIGS. 8-9D.

In some embodiments, the crystal may have a backing that may minimallyaffects the Q-factor of the crystal (e.g. less than 5%). The backing maybe made of a substantially acoustically transparent material such asbalsa wood, foam, or cork which allows the crystal to vibrate in ahigher order mode shape and maintains a high Q-factor while stillproviding some mechanical support for the crystal. The backing layer maybe a solid, or may be a lattice having holes through the layer, suchthat the lattice follows the nodes of the vibrating crystal in aparticular higher order vibration mode, providing support at nodelocations while allowing the rest of the crystal to vibrate freely. Thegoal of the lattice work or acoustically transparent material is toprovide support without lowering the Q-factor of the crystal orinterfering with the excitation of a particular mode shape.

Placing the crystal in direct contact with the fluid also contributes tothe high Q-factor by avoiding the dampening and energy absorptioneffects of the epoxy layer and the wear plate. Other embodiments mayhave wear plates or a wear surface to prevent the PZT, which containslead, contacting the host fluid. The insertion of a layer over the PZTmay be desirable in, for example, biological applications such asseparating blood. Such applications might use a wear layer such aschrome, electrolytic nickel, or electroless nickel. Chemical vapordeposition could also be used to apply a layer of poly(p-xylylene) (e.g.Parylene) or other polymer. Organic and biocompatible coatings such assilicone or polyurethane are also usable as a wear surface. A glassycarbon wear layer may also be utilized. Glassy carbon, also known asvitreous carbon, is a non-graphitizing carbon which combines both glassyand ceramic properties with those of graphite. The most importantproperties are high temperature resistance, hardness (7 Mohs), lowdensity, low electrical resistance, low friction and low thermalresistance. Glassy carbon also has extreme resistance to chemical attackand impermeability to gases and liquids.

In the present disclosure, the piezoelectric crystal used in eachultrasonic transducer is modified to be in the form of a segmented arrayof piezoelectric elements. This array is used to form a multidimensionalacoustic standing wave or waves, which can be used for acoustophoresis.

FIG. 4 shows a monolithic, one-piece, single electrode piezoelectriccrystal 200 that is used in ultrasonic transducers. The piezoelectriccrystal has a substantially square shape, with a length 203 and a width205 that are substantially equal to each other (e.g. about one inch).The crystal 200 has an inner surface 202, and the crystal also has anouter surface 204 on an opposite side of the crystal which is usuallyexposed to fluid flowing through the acoustophoretic device. The outersurface and the inner surface are relatively large in area, and thecrystal is relatively thin (e.g. about 0.040 inches for a 2 MHzcrystal).

FIG. 5 shows a piezoelectric crystal 200′ of the present disclosure. Theinner surface 202 of this piezoelectric crystal 200′ is divided into apiezoelectric array 206 with a plurality of (i.e. at least two)piezoelectric elements 208. However, the array is still a singlecrystal. The piezoelectric elements 208 are separated from each other byone or more channels or kerfs 210 in the inner surface 202. The width ofthe channel (i.e. between piezoelectric elements) may be on the order offrom about 0.001 inches to about 0.02 inches. The depth of the channelcan be from about 0.001 inches to about 0.02 inches. In some instances,a potting material 212 (i.e., epoxy, Sil-Gel, and the like) can beinserted into the channels 210 between the piezoelectric elements. Thepotting material 212 is non-conducting, acts as an insulator betweenadjacent piezoelectric elements 208, and also acts to hold the separatepiezoelectric elements 208 together. Here, the array 206 containssixteen piezoelectric elements 208 (although any number of piezoelectricelements is possible), arranged in a rectangular 4×4 configuration(square is a subset of rectangular). Each of the piezoelectric elements208 has substantially the same dimensions as each other. The overallarray 200′ has the same length 203 and width 205 as the single crystalillustrated in FIG. 4.

FIG. 6 shows another embodiment of a transducer 200″. The transducer200″ is substantially similar to the transducer 200′ of FIG. 5, exceptthat the array 206 is formed from twenty-five piezoelectric elements 208in a 5×5 configuration. Again, the overall array 200″ has the samelength 203 and width 205 as the single crystal illustrated in FIG. 4.

Each piezoelectric element in the piezoelectric array of the presentdisclosure may have individual electrical attachments (i.e. electrodes),so that each piezoelectric element can be individually controlled forfrequency and power. These elements can share a common ground electrode.This configuration allows for not only the generation of amulti-dimensional acoustic standing wave, but also improved control ofthe acoustic standing wave.

The piezoelectric array can be formed from a monolithic piezoelectriccrystal by making cuts across one surface so as to divide the surface ofthe piezoelectric crystal into separate elements. The cutting of thesurface may be performed through the use of a saw, an end mill, or othermeans to remove material from the surface and leave discrete elements ofthe piezoelectric crystal between the channels/grooves that are thusformed.

As explained above, a potting material may be incorporated into thechannels/grooves between the elements to form a composite material. Forexample, the potting material can be a polymer, such as epoxy. Inparticular embodiments, the piezoelectric elements 208 are individuallyphysically isolated from each other. This structure can be obtained byfilling the channels 210 with the potting material, then cutting,sanding or grinding the outer surface 204 down to the channels. As aresult, the piezoelectric elements are joined to each other through thepotting material, and each element is an individual component of thearray. Put another way, each piezoelectric element is physicallyseparated from surrounding piezoelectric elements by the pottingmaterial. FIG. 21 is a cross-sectional view comparing these twoembodiments. On top, a crystal as illustrated in FIG. 5 is shown. Thecrystal is kerfed into four separate piezoelectric elements 208 on theinner surface 202, but the four elements share a common outer surface204. On the bottom, the four piezoelectric elements 208 are physicallyisolated from each other by potting material 212. No common surface isshared between the four elements.

In the present systems, the system is operated at a voltage such thatthe particles are trapped in the ultrasonic standing wave, i.e., remainin a stationary position. The particles are collected in along welldefined trapping lines, separated by half a wavelength. Within eachnodal plane, the particles are trapped in the minima of the acousticradiation potential. The axial component of the acoustic radiation forcedrives the particles, with a positive contrast factor, to the pressurenodal planes, whereas particles with a negative contrast factor aredriven to the pressure anti-nodal planes. The radial or lateralcomponent of the acoustic radiation force is the force that traps theparticle. In systems using typical transducers, the radial or lateralcomponent of the acoustic radiation force is typically several orders ofmagnitude smaller than the axial component of the acoustic radiationforce. However, the lateral force in the devices of the presentdisclosure can be significant, on the same order of magnitude as theaxial force component, and is sufficient to overcome the fluid dragforce at linear velocities of up to 1 cm/s. As discussed above, thelateral force can be increased by driving the transducer in higher ordermode shapes, as opposed to a form of vibration where the crystaleffectively moves as a piston having a uniform displacement. Theacoustic pressure is proportional to the driving voltage of thetransducer. The electrical power is proportional to the square of thevoltage.

During operation, the piezoelectric arrays of the present disclosure canbe driven so that the piezoelectric elements are in phase with eachother. In other words, each piezoelectric element creates amulti-dimensional acoustic standing wave that has the same frequency andno time shift. In other embodiments, the piezoelectric elements can beout of phase with each other, i.e. there is a different frequency ortime shift, or they have a different phase angle. As described furtherbelow, in more specific embodiments the elements in the array arearranged in groups or sets that are out of phase by multiples of 90°(i.e. 90° and/or 180°).

In embodiments, the pulsed voltage signal driving the transducer canhave a sinusoidal, square, sawtooth, or triangle waveform; and have afrequency of 500 kHz to 10 MHz. The pulsed voltage signal can be drivenwith pulse width modulation, which produces any desired waveform. Thepulsed voltage signal can also have amplitude or frequency modulationstart/stop capability to eliminate streaming.

FIG. 7 is a lin-log graph (linear y-axis, logarithmic x-axis) that showsthe calculated scaling of the acoustic radiation force, fluid dragforce, and buoyancy force with particle radius. The buoyancy force isapplicable to negative contrast factor particles, such as oil particlesin this example. The calculated buoyancy force may include elements ofgravity forces. In examples using positive contrast factor particles,which may be some types of cells, a line indicating gravity forces isused in a graph for such positive contrast factor particles showingacoustic radiation force and fluid drag force. In the present exampleillustrated in FIG. 7 calculations are done for a typical SAE-30 oildroplet used in experiments. The buoyancy force is a particle volumedependent force, e.g., proportional to the radius cubed, and isrelatively negligible for particle sizes on the order of a micron, butgrows, and becomes significant for particle sizes on the order ofhundreds of microns. The fluid drag force scales linearly with fluidvelocity, e.g., proportional to the radius squared, and typicallyexceeds the buoyancy force for micron sized particles, but is lessinfluential for larger sized particles on the order of hundreds ofmicrons. The acoustic radiation force scaling acts differently than thefluid drag force or the buoyancy force. When the particle size is small,the acoustic trapping force scales with the cube of the particle radius(volume) of the particle at a close to linear rate. Eventually, as theparticle size grows, the acoustic radiation force no longer increaseslinearly with the cube of the particle radius. As the particle sizecontinues to increase, the acoustic radiation force rapidly diminishesand, at a certain critical particle size, is a local minimum. Forfurther increases of particle size, the radiation force increases againin magnitude but with opposite phase (not shown in the graph). Thispattern repeats for increasing particle sizes. The particle size toacoustic radiation force relationship is at least partially dependent onthe wavelength or frequency of the acoustic standing wave. For example,as a particle increases to a half-wavelength size, the acousticradiation force on the particle decreases. As a particle size increasesto greater than a half-wavelength and less than a full wavelength, theacoustic radiation force on the particle increases.

Initially, when a suspension is flowing through the acoustic standingwave with primarily small micron sized particles, the acoustic radiationforce balances the combined effect of fluid drag force and buoyancyforce to trap a particle in the standing wave. In FIG. 7, trappingoccurs for a particle size of about 3.5 micron, labeled as Rd. Inaccordance with the graph in FIG. 7, as the particle size continues toincrease beyond Rd, larger particles are trapped, as the acousticradiation force increases compared to the fluid drag force. As smallparticles are trapped in the standing wave, particlecoalescence/clumping/aggregation/agglomeration takes place, resulting incontinuous growth of effective particle size. Other, smaller particlescontinue to be driven to trapping sites in the standing wave as thelarger particles are held and grow in size, contributing to continuoustrapping. As the particle size grows, the acoustic radiation force onthe particle increases, until a first region of particle size isreached. As the particle size increases beyond the first region, theacoustic radiation force on the particle begins to decrease. As particlesize growth continues, the acoustic radiation force decreases rapidly,until the buoyancy force becomes dominant, which is indicated by asecond critical particle size, R_(c2), at which size the particles riseor sink, depending on their relative density or acoustic contrast factorwith respect to the host fluid. As the particles rise or sink and leavethe antinode (in the case of negative contrast factor) or node (in thecase of positive contrast factor) of the acoustic standing wave, theacoustic radiation force on the particles may diminish to a negligibleamount. The acoustic radiation force continues to trap small and largeparticles, and drive the trapped particles to a trapping site, which islocated at a pressure antinode in this example. The smaller particlesizes experience a reduced acoustic radiation force, which, for example,decreases to that indicated near point R_(c1). As other particles aretrapped and coalesce, clump, aggregate, agglomerate and/or clustertogether at the node or antinode of the acoustic standing wave,effectively increasing the particle size, the acoustic radiation forceincreases and the cycle repeats. All of the particles may not drop outof the acoustic standing wave, and those remaining particles maycontinue to grow in size. Thus, FIG. 7 explains how small particles canbe trapped continuously in a standing wave, grow into larger particlesor clumps, and then eventually rise or settle out because of therelationship between buoyancy force, drag force and acoustic radiationforce with respect to particle size.

The size, shape, and thickness of the transducer determine thetransducer displacement at different frequencies of excitation, which inturn affects oil separation efficiency. Typically, the transducer isoperated at frequencies near the thickness resonance frequency (halfwavelength). Gradients in transducer displacement typically result inmore places for oil to be trapped. Higher order modal displacementsgenerate three-dimensional acoustic standing waves with strong gradientsin the acoustic field in all directions, thereby creating equally strongacoustic radiation forces in all directions, leading to multipletrapping lines, where the number of trapping lines correlate with theparticular mode shape of the transducer.

FIG. 8 shows the measured electrical impedance amplitude of a 1″ squarePZT-8 2-MHz transducer as a function of frequency in the vicinity of the2.2 MHz transducer resonance. The minima in the transducer electricalimpedance correspond to acoustic resonances of the water column andrepresent potential frequencies for operation. Numerical modeling hasindicated that the transducer displacement profile varies significantlyat these acoustic resonance frequencies, and thereby directly affectsthe acoustic standing wave and resulting trapping force. Since thetransducer operates near its thickness resonance, the displacements ofthe electrode surfaces are essentially out of phase. The typicaldisplacement of the transducer electrodes is not uniform and variesdepending on frequency of excitation. As an example, at one frequency ofexcitation with a single line of trapped oil droplets, the displacementhas a single maximum in the middle of the electrode and minima near thetransducer edges. At another excitation frequency, the transducerprofile has multiple maxima leading to multiple trapped lines of oildroplets. Higher order transducer displacement patterns result in highertrapping forces and multiple stable trapping lines for the captured oildroplets.

To investigate the effect of the transducer displacement profile onacoustic trapping force and oil separation efficiencies, an experimentwas repeated ten times, with all conditions identical except for theexcitation frequency. Ten consecutive acoustic resonance frequencies,indicated by circled numbers 1-9 and letter A on FIG. 8, were used asexcitation frequencies. These oscillations in the impedance correspondto the resonance of the acoustophoretic system. With the length of theacoustophoretic system being 2″, the oscillations are spaced about 15kHz apart. The conditions were experiment duration of 30 min, a 1000 ppmoil concentration of approximately 5-micron SAE-30 oil droplets, a flowrate of 500 ml/min, and an applied power of 20 Win a 1-inch wide×2-inchlong cross-section.

As the emulsion passed by the transducer, the trapping lines of oildroplets were observed and characterized. The characterization involvedthe observation and pattern of the number of trapping lines across thefluid channel, as shown in FIG. 9A, for seven of the ten resonancefrequencies identified in FIG. 8.

FIG. 9B shows an isometric view of the system in which the trapping linelocations are being determined. FIG. 9C is a view of the system as itappears when looking down the inlet, along arrow 114. FIG. 9D is a viewof the system as it appears when looking directly at the transducerface, along arrow 116. The trapping lines shown in FIGS. 9B-9D are thoseproduced at frequency 4 in FIG. 8 and FIG. 9A.

The effect of excitation frequency clearly determines the number oftrapping lines, which vary from a single trapping line at the excitationfrequency of acoustic resonance 5 and 9, to nine trapping lines foracoustic resonance frequency 4. At other excitation frequencies four orfive trapping lines are observed. Different displacement profiles of thetransducer can produce different (more) trapping lines in the standingwaves, with more gradients in displacement profile generally creatinghigher trapping forces and more trapping lines.

Table 1 summarizes the findings from an oil trapping experiment using asystem similar to FIG. 10A. An important conclusion is that the oilseparation efficiency of the acoustic separator is directly related tothe mode shape of the transducer. Higher order displacement profilesgenerate larger acoustic trapping forces and more trapping linesresulting in better efficiencies. A second conclusion, useful forscaling studies, is that the tests indicate that capturing 5 micron oildroplets at 500 ml/min implies 10 Watts of power per square-inch oftransducer area per 1″ of acoustic beam span. The main dissipation isthat of thermo-viscous absorption in the bulk volume of the acousticstanding wave. The cost of energy associated with this flow rate is0.500 kWh per cubic meter.

TABLE 1 Trapping Pattern Capture Efficiency Study Total Resonance Power# of Flow Capture Peak Input Trapping rate Duration Efficiency Location(Watts) Lines (ml/min) (min) (%) 4 20 9 500 30 91% 8 20 5 500 30 58% A20 4 500 30 58% 9 20 2 500 30 37%

A 4″ by 2.5″ flow cross sectional area intermediate scale apparatus 124for separating a host fluid from a buoyant fluid or particulate is shownin FIG. 10A. The acoustic path length is 4″. The apparatus is shown herein an orientation where the flow direction is downwards, which is usedfor separating less-dense particles from the host fluid. However, theapparatus may be essentially turned upside down to allow separation ofparticles which are heavier than the host fluid. Instead of a buoyantforce in an upward direction, the weight of the agglomerated particlesdue to gravity pulls them downward. It should be noted that thisembodiment is depicted as having an orientation in which fluid flowsvertically. However, it is also contemplated that fluid flow may be in ahorizontal direction, or at an angle.

A particle-containing fluid enters the apparatus through inlets 126 intoan annular plenum 131. The annular plenum has an annular inner diameterand an annular outer diameter. It is noted that the term “annular” isused here to refer to the area between two shapes, and the plenum doesnot need to be circular. Two inlets are visible in this illustration,though it is contemplated that any number of inlets may be provided asdesired. In particular embodiments, four inlets are used. The inlets areradially opposed and oriented.

A contoured nozzle wall 129 reduces the outer diameter of the flow pathin a manner that generates higher velocities near the wall region andreduces turbulence, producing near plug flow as the fluid velocityprofile develops, i.e. the fluid is accelerated downward in thedirection of the centerline with little to no circumferential motioncomponent and low flow turbulence. This chamber flow profile isdesirable for acoustic separation and particle collection. The fluidpasses through connecting duct 127 and into a flow/separation chamber128. As seen in the zoomed-in contoured nozzle 129 in FIG. 10B, thenozzle wall also adds a radial motion component to the suspendedparticles, moving the particles closer to the centerline of theapparatus and generating more collisions with rising, buoyantagglomerated particles. This radial motion will allow for optimumscrubbing of the particles from the fluid in the connecting duct 127prior to reaching the separation chamber. The contoured nozzle wall 129directs the fluid in a manner that generates large scale vortices at theentrance of the collection duct 133 to also enhance particle collection.Generally, the flow area of the device 124 is designed to be continuallydecreasing from the annular plenum 131 to the separation chamber 128 toassure low turbulence and eddy formation for better particle separation,agglomeration, and collection. The nozzle wall has a wide end and anarrow end. The term scrubbing is used to describe the process ofparticle/droplet agglomeration, aggregation, clumping or coalescing,that occurs when a larger particle/droplet travels in a directionopposite to the fluid flow and collides with smaller particles, ineffect scrubbing the smaller particles out of the suspension.

Returning to FIG. 10A, the flow/separation chamber 128 includes atransducer array 130 and reflector 132 on opposite sides of the chamber.In use, multi-dimensional standing waves 134 are created between thetransducer array 130 and reflector 132. These standing waves can be usedto agglomerate particles, and this orientation is used to agglomerateparticles that are buoyant (e.g. oil). Fluid, containing residualparticles, then exits through flow outlet 135.

As the buoyant particles agglomerate, they eventually overcome thecombined effect of the fluid flow drag forces and acoustic radiationforce, and their buoyant force 136 is sufficient to cause the buoyantparticles to rise upwards. In this regard, a collection duct 133 issurrounded by the annular plenum 131. The larger particles will passthrough this duct and into a collection chamber 140. This collectionchamber can also be part of an outlet duct. The collection duct and theflow outlet are on opposite ends of the apparatus.

It should be noted that the buoyant particles formed in the separationchamber 128 subsequently pass through the connecting duct 127 and thenozzle wall 129. This arrangement causes the incoming flow from theannular plenum to flow over the rising agglomerated particles due to theinward radial motion imparted by the nozzle wall.

The transducer setup of the present disclosure creates athree-dimensional pressure field which includes standing wavesperpendicular to the fluid flow. The pressure gradients are large enoughto generate acoustophoretic forces in a lateral direction, e.g.,orthogonal to the standing wave direction (i.e., the acoustophoreticforces are parallel to the fluid flow direction) which are of the sameorder of magnitude as the acoustophoretic forces in the wave direction.These forces permit enhanced particle trapping, clumping and collectionin the flow chamber and along well-defined trapping lines, as opposed tomerely trapping particles in collection planes as in conventionaldevices. The particles have significant time to move to nodes oranti-nodes of the standing waves, generating regions where the particlescan concentrate, agglomerate, and/or coalesce, and then buoyancy/gravityseparate.

In some embodiments, the fluid flow has a Reynolds number of up to 1500,i.e. laminar flow is occurring. For practical application in industry,the Reynolds number is usually from 10 to 1500 for the flow through thesystem. The particle movement relative to the fluid motion generates aReynolds number much less than 1.0. The Reynolds number represents theratio of inertial flow effects to viscous effects in a given flow field.For Reynolds numbers below 1.0, viscous forces are dominant in the flowfield. This situation results in significant damping where shear forcesare predominant throughout the flow. This flow where viscous forces aredominant is called Stokes flow. The flow of molasses is an example. Wallcontouring and streamlining have very little importance under suchconditions. These characteristics are associated with the flow of veryviscous fluids or the flow in very tiny passages, like MEMS devices.Inlet contouring has little importance. The flow of the particlesrelative to the fluid in an acoustophoretic particle separator will beStokes flow because both the particle diameters and the relativevelocities between the particles and fluid are very small. On the otherhand, the Reynolds number for the flow through the system will be muchgreater than 1.0 because the fluid velocity and inlet diameter are muchlarger.

For Reynolds numbers much greater than 1.0, viscous forces are dominantwhere the flow is in contact with the surface. This viscous region nearthe surface is called a boundary layer and was first recognized byLudwig Prandtl. In duct flow, the flow will be laminar if the Reynoldsnumber is significantly above 1.0 and below 2300 for fully developedflow in the duct. The wall shear stress at the wall will diffuse intothe stream with distance. At the inlet of the duct, flow velocity startsoff uniform. As the flow moves down the duct, the effect of wall viscousforces will diffuse inward towards the centerline to generate aparabolic velocity profile. This parabolic profile will have a peakvalue that is twice the average velocity. The length of duct for theparabolic profile to develop is a function of the Reynolds number. For aReynolds number of 20, which is typical for CHO operation, thedevelopment length will be 1.2 duct diameters. Thus, fully developedflow happens very quickly. This peak velocity in the center can bedetrimental to acoustic particle separation. Also, at laminar flowReynolds numbers turbulence, can occur and flow surface contouring isvery important in controlling the flow. For these reasons, the separatorwas designed with an annular inlet plenum and collector tube.

The large annular plenum is followed by an inlet wall nozzle thataccelerates and directs the fluid inward toward the centerline as shownin FIG. 10B. The wall contour will have a large effect on the profile.The area convergence increases the flow average velocity, but it is thewall contour that determines the velocity profile. The nozzle wallcontour will be a flow streamline, and is designed with a small radiusof curvature in the separator.

The transducer(s) is/are used to create a pressure field that generatesforces of the same order of magnitude both orthogonal to the standingwave direction and in the standing wave direction. When the forces areroughly the same order of magnitude, particles of size 0.1 microns to300 microns will be moved more effectively towards regions ofagglomeration (“trapping lines”). Because of the equally large gradientsin the orthogonal acoustophoretic force component, there are “hot spots”or particle collection regions that are not located in the regularlocations in the standing wave direction between the transducer 130 andthe reflector 132. Hot spots are located at the minima of acousticradiation potential. Such hot spots represent particle collectionlocations.

One application of the acoustophoretic device is the separation of abiological therapeutic protein from the biologic cells that produce theprotein. In this regard, current methods of separation use filtration orcentrifugation, either of which can damage cells, releasing proteindebris and enzymes into the purification process and increasing the loadon downstream portions of the purification system. It is desirable to beable to process volumes having higher cell densities, because thispermits collection of larger amounts of the therapeutic protein andbetter cost efficiencies.

FIG. 11A and FIG. 11B are exploded views showing the various parts ofacoustophoretic separators. FIG. 11A has only one separation chamber,while FIG. 11B has two separation chambers.

Referring to FIG. 11A, fluid enters the separator 190 through afour-port inlet 191. An annular plenum is also visible here. Atransition piece 192 is provided to create plug flow through theseparation chamber 193. This transition piece includes a contourednozzle wall, like that described above in FIG. 10A, which has a curvedshape. A transducer 40 and a reflector 194 are located on opposite wallsof the separation chamber. Fluid then exits the separation chamber 193and the separator through outlet 195. The separation chamber has arectangular-shaped flow path geometry.

FIG. 11B has two separation chambers 193. A system coupler 196 is placedbetween the two chambers 193 to join them together.

Acoustophoretic separation has been tested on different lines of Chinesehamster ovary (CHO) cells. In one experiment, a solution with a startingcell density of 8.09×106 cells/mL, a turbidity of 1,232 NTU, and cellviability of roughly 75% was separated using a system as depicted inFIG. 11A. The transducers were 2 MHz crystals, run at approximately 2.23MHz, drawing 24-28 Watts. A flow rate of 25 mL/min was used. The resultof this experiment is shown in FIG. 12A.

In another experiment, a solution with a starting cell density of8.09×106 cells/mL, a turbidity of 1,232 NTU, and cell viability ofroughly 75% was separated. This CHO cell line had a bi-modal particlesize distribution (at size 12 μm and 20 μm). The result is shown in FIG.12B.

FIG. 12A and FIG. 12B were produced by a Beckman Coulter Cell ViabilityAnalyzer. Other tests revealed that frequencies of 1 MHz and 3 MHz werenot as efficient as 2 MHz at separating the cells from the fluid.

In other tests at a flow rate of 10 L/hr, 99% of cells were capturedwith a confirmed cell viability of more than 99%. Other tests at a flowrate of 50 mL/min (i.e. 3 L/hr) obtained a final cell density of 3×106cells/mL with a viability of nearly 100% and little to no temperaturerise. In yet other tests, a 95% reduction in turbidity was obtained at aflow rate of 6 L/hr.

Testing on the scaled unit shown in FIG. 10A-10B was performed usingyeast as a simulant for CHO for the biological applications. For thesetests, at a flow rate of 15 L/hr, various frequencies were tested aswell as power levels. Table 2 shows the results of the testing.

TABLE 2 2.5″ × 4″ System results at 15 L/hr Flow rate Frequency (MHz) 30Watts 37 Watts 45 Watts 2.2211 93.9 81.4 84.0 2.2283 85.5 78.7 85.42.2356 89.1 85.8 81.0 2.243 86.7 — 79.6

In biological applications, many parts, e.g. the tubing leading to andfrom the housing, inlets, exit plenum, and entrance plenum, may all bedisposable, with only the transducer and reflector to be cleaned forreuse. Avoiding centrifuges and filters allows better separation of theCHO cells without lowering the viability of the cells. The form factorof the acoustophoretic separator is also smaller than a filteringsystem, allowing the CHO separation to be miniaturized. The transducersmay also be driven to create rapid pressure changes to prevent or clearblockages due to agglomeration of CHO cells. The frequency of thetransducers may also be varied to obtain optimal effectiveness for agiven power.

The following examples are provided to illustrate the apparatuses,components, and methods of the present disclosure. The examples aremerely illustrative and are not intended to limit the disclosure to thematerials, conditions, or process parameters set forth therein.

EXAMPLES

A two-dimensional numerical model was developed for the acoustophoreticdevice using COMSOL simulation software. The model is illustrated inFIG. 13. The device included an aluminum wall 222, and a stainless steelreflector 224 opposite the wall. Embedded in the wall was apiezoelectric transducer 230. As illustrated here, the transducer is inthe form of a 4-element piezoelectric array. The wall 222 and thereflector 224 define a flow chamber, with arrow 225 indicating the flowdirection of fluid through the chamber. The piezoelectric transducer wasin direct contact with the fluid. Channels/kerfs 210 and pottingmaterial 212 are also illustrated, though potting material was not usedin the simulation.

The simulation software was run, and its output was compared topublished data (Barmatz, J. Acoust. Soc. Am. 77, 928, 1985). FIG. 14Acompares the acoustic potential U. FIG. 14B compares the x-component ofthe acoustic radiation force (ARF). FIG. 14C compares the y-component ofthe ARF. FIG. 14D compares the absolute value of the ARF. In thesefigures, the published data is on the top, while the numerical modelresults are on the bottom. As can be seen here, the results of thenumerical model match the published data, which validates the numericalmodel and subsequent calculations made therefrom.

Three different simulations were then run to model the separation of SAE30 oil droplets from water using three different piezoelectrictransducers: a 1-element transducer (i.e. single crystal), a 4-elementtransducer, and a 5-element transducer. The transducers were operated atthe same frequency, and the following parameters were used for the oiland the water:oil particle radius (R_(P))=10 μm; oil density (ρ_(p))=865kg/m3; speed of sound in oil (c_(p))=1750 m/sec; particle velocity(μf)=0.001 kg/msec; water density (ρ_(f))=1000 kg/m3; and speed of soundin water (c_(f))=1500 m/sec.

For the 4-element transducer, each channel had a width of 0.0156 inchesand a depth of 0.0100 inches, and each element had a width of 0.2383inches (total width of the transducer was one inch). For the 5-elementtransducer, each channel had a width of 0.0156 inches and a depth of0.0100 inches, and each element had a width of 0.1875 inches.

FIG. 15 shows the simulation of the forces on a particle using the1-element transducer, which is a two-dimensional representation of PZTcrystal 200. FIG. 16 shows the simulation of the forces on a particleusing the 4-element transducer, which is a two-dimensionalrepresentation of PZT crystal 200′. FIG. 17 shows the simulation of theforces on a particle using the 5-element transducer, which is atwo-dimensional representation of PZT crystal 200″. Each transducer hadthe same width, regardless of the number of elements. The amplitude ofthe multi-dimensional acoustic standing waves generated therefrom areclearly seen (lighter area is higher amplitude than darker area).

Next, simulations were run on a 4-element array to compare the effect ofthe phase on the waves. The flow rate was 500 mL/min, the Reynoldsnumber of the fluid was 220, the input voltage per element was 2.5 VDC,and the DC power per element was 1 watt. In one simulation, the fourelements were in a 0-180-0-180 phase (i.e. out of phase) with respect toeach other. In another simulation, the four elements were all in phasewith each other. The simulations were then compared to actualexperiments conducted with a transducer device having a 4×4piezoelectric array as in FIG. 18.

FIG. 19 compares the results of the out-of-phase simulation (left) witha picture (right) showing the actual results when an out-of-phase arraywas used in the transducer device of FIG. 18. The results are verysimilar. Where the amplitude is high in the simulation, trappedparticles are seen in the actual picture.

FIG. 20 compares the results of the in-phase simulation (left) with apicture (right) showing the actual results when an in-phase array wasused in the transducer device of FIG. 18. The results are very similar.

Additional numerical models were performed with the 4-element transducerand the 5-element transducer, either in-phase or out-of-phase indifferent arrangements, as described in Table 3 below, over a frequencysweep of 2.19 MHz to 2.25 MHz, for oil droplets of diameter 20 microns.Out-of-phase means that adjacent elements are excited with differentphases.

FIG. 22 is a diagram illustrating the two out-of-phase modes that weresimulated for the 4-element array. The left-hand side illustrates the0-180-0-180 mode, while the right-hand side illustrated the 0-180-180-0mode. FIG. 23 is a diagram illustrating the four out-of-phase modes thatwere simulated for the 5-element array. The top left picture illustratesthe 0-180-0-180-0 mode. The top right picture illustrates the0-0-180-0-0 mode. The bottom left picture illustrates the0-180-180-180-0 mode. The bottom right picture illustrates the0-90-180-90-0 mode.

The ratio of the lateral (x-axis) force component to the axial (y-axis)force component of the acoustic radiation force was determined over thisfrequency range, and the range of that ratio is listed in Table 3 below.

TABLE 3 Transducer Phase Ratio Min Ratio Max 1-Element (single crystal)~0.15 ~0.75 4-Element Array In-Phase ~0.08 ~0.54 4-Element Array(0-180-0-180) ~0.39 ~0.94 4-Element Array (0-180-180-0) ~0.39 ~0.925-Element Array In-Phase ~0.31 ~0.85 5-Element Array (0-180-0-180-0)~0.41 ~0.87 5-Element Array (0-0-180-0-0) ~0.41 ~0.81 5-Element Array(0-180-180-180-0) ~0.40 ~0.85 5-Element Array (0-90-180-90-0) ~0.38~0.81

FIG. 24 shows the normalized acoustic radiation force (ARF) from thesingle piezoelectric crystal simulation. The ARF value was normalizedwith the real power calculated with the measured voltage and current.FIG. 25 shows the ratio of the ARF components (lateral to axial) for thesingle piezoelectric crystal simulation over the tested frequency range.FIG. 26 shows the normalized acoustic radiation force (ARF) from the5-element simulation. FIG. 27 shows the ratio of the ARF components(lateral to axial) for the 5-element simulation over the testedfrequency range. Comparing FIG. 24 to FIG. 26, the peak ARF for the1-element simulation is about 6e-11, while the peak ARF for the5-element simulation is about 2e-9. Comparing FIG. 25 to FIG. 27, theratio of the forces is also more consistent, with a variation of about0.60 compared to about 0.40.

Generally, the 4-element and 5-element arrays produced high ratios,including some greater than 0.9. Some of the simulations also hadacoustic radiation force amplitudes that were almost two orders ofmagnitude higher than those produced by the 1-element transducer (whichserved as the baseline).

Experimental 16-element arrays and 25-element arrays were then tested.The feed solution was a 3% packed cell mass yeast solution, used as asimulant for CHO cells for biological applications. For out-of-phasetesting, a checkerboard pattern of 0° and 180° phases was used. For the25-element array, 12 elements were at 180° and 13 elements were at 0°.These checkerboard patterns are illustrated in FIG. 28. The left-handside is the 16-element array and the right-hand side is the 25-elementarray, with the different shades indicating the different phase angle.

The turbidity of the feed, concentrate, and permeate were measured after30 minutes at various frequencies. The concentrate was the portionexiting the device that contained the concentrated yeast, along withsome fluid. The permeate was the filtered portion exiting the device,which was mostly liquid with a much lower concentration of yeast. Alower turbidity indicated a lower amount of yeast. The captureefficiency was determined as (feed-permeate)/feed*100%. The feed ratewas 30 mL/min, and the concentrate flow rate was 5 mL/min. The power tothe transducers was set at 8 W.

Table 4 lists results for the single-element transducer, which is usedas a baseline or control.

TABLE 4 Frequency (MHz) 2.225 2.244 Concentrate (NTU) 15,400 15,400Permeate (NTU) 262 327 Feed (NTU) 4,550 5,080 Capture Efficiency (%)94.2 93.6

Table 5 lists results for the 16-element in-phase experiments.

TABLE 5 Frequency (MHz) 2.22 2.225 2.23 2.242 2.243 2.244 2.255 2.26Concentrate (NTU) 22,700 24,300 22,500 24,600 23,100 28,100 27,40023,800 Permeate (NTU) 205 233 241 201 249 197 244 165 Feed (NTU) 5,0804,850 5,100 4,830 4,810 5,080 4,940 4,830 Capture Efficiency 96.0 95.295.3 95.8 94.8 96.1 95.1 96.6 (%)

Table 6 lists results for the 16-element out-of-phase experiments.

TABLE 6 Frequency (MHz) 2.22 2.225 2.23 2.242 2.243 2.244 2.255 2.26Concentrate (NTU) 40,900 21,400 26,000 49,300 19,100 55,800 22,10035,000 Permeate (NTU) 351 369 382 1,690 829 761 397 581 Feed (NTU) 5,5904,870 5,860 5,160 5,040 4,870 4,800 5,170 Capture Efficiency 93.7 92.493.5 67.2 83.6 84.4 91.7 88.8 (%)

Comparing the 16-element array results to each other and the control,the in-phase array maintains high capture efficiency through thefrequency range, while the out-of-phase array drops off quickly around2.24 MHz. The efficiency results are very similar to the control formost in-phase tests. The in-phase efficiency was higher than theout-of-phase efficiency at every frequency.

Table 7 lists results for the 25-element in-phase experiments.

TABLE 7 Frequency (MHz) 2.2190 2.2300 2.2355 2.2470 2.2475 2.2480 2.24852.2615 Concentrate (NTU) 13,300 19,800 20,900 21,400 13,700 17,30019,000 19,500 Permeate (NTU) 950 669 283 1,044 1,094 1,164 688 797 Feed(NTU) 4,930 4,930 4,910 5,010 4,950 5,220 5,010 5,110 Capture Efficiency80.7 86.4 94.2 79.2 77.9 77.7 86.3 84.4 (%)

Table 8 lists results for the 25-element out-of-phase experiments.

TABLE 8 Frequency (MHz) 2.2190 2.2300 2.2355 2.2470 2.2475 2.2480 2.24852.2615 Concentrate (NTU) 14,605 — 21,700 18,025 23,425 22,575 21,90022,450 Permeate (NTU) 2,568 2,541 1,484 1,134 1,005 987 905 2,034 Feed(NTU) 5,610 6,020 5,200 6,010 5,880 5,840 5,860 5,880 Capture Efficiency54.2 57.8 71.5 81.1 82.9 83.1 84.6 65.4 (%)

Comparing the 25-element array results to each other and the control,both arrays are less efficient than the control. The 25-element in-phasearray peaks around 95% and then drops off in both directions. Theout-of-phase array peaks around 85% efficiency and drops off sharply.The efficiency results are very similar to the control. It should benoted that the high peak amplitudes found using the numerical model havenot been tested experimentally.

FIG. 29 is a circuit diagram of an RF power supply 300 with an LCLfilter network 302 that provides a transducer drive signal on a line 304to an ultrasonic transducer 306. In this embodiment, a DC-DC converter308 receives a first DC voltage from a source 310 and switches 312, 314(e.g., power MOSFETs) are cooperatively switched under the control of acontroller (not shown) to generate a pulse width modulated (PWM) signalthat is provided on a line 316. The switches 312, 314 are driven byfirst complementary clocking signals generated by the controller, andhave the same frequency and duty cycle. The switches may not be closedat the same time, and the switching action produces a chopped voltageV_(b) across the switch 314. The resultant PWM signal on the line 316 isreceived by a filter 318 (e.g., a buck filter) that filters the signalon the line 318 so the average voltage appears across capacitor C₂ 320,and is provided on line 322 to a DC-AC inverter 324. The bandwidth ofthe filter 318 is selected so the voltage on the line 322 followschanges in the duty cycle of the clocking signals that drive theswitches 312, 314 based upon dynamic changes in acoustic cavity 326.Second complementary clocking signals generated by the controller driveswitches 328, 330 to perform the DC to AC inversion, and a resultant ACsignal is provided on line 332. The AC signal is then input to thematching filter network 302 (e.g., an LC, LCL, et cetera) which filtersthe input to attenuate higher frequency components of the input andprovide a periodic signal such a sine wave on the line 304 to drive thetransducer 306. In this embodiment, the LCL filter 302 includes seriallyconnected inductors L2, L2, 334, 336, respectively and a capacitor C3338 that extends from a node between the inductors 334, 336 to ground.LCL circuit 302 filters the output of the inverter 324 and matches thetransducer 306 to the inverter 324 for improved power transfer.

The matching filter 302 provides impedance scaling to obtain anappropriate load for the inverter drive. The matching filter can beconsidered a network, which is tuned to provide desired power transfer,such as optimized power transfer, through the transducer 306 and intothe resonant cavity 326. Considerations for implementing the filter 302(e.g., LC or LCL) include the combined response of the transducer 306and the resonant cavity 326. According to one example, the filterpermits desired power transfer, such as optimized power transfer, whenthe acoustic transducer is operated in a multi-dimensional mode, or in amulti-mode, for example, with multiple overlaid vibrational modes thatproduce one or more primary or dominant vibrational modes. A desiredmode of operation is at a frequency that corresponds to a low or minimumreactance point of the response of the transducer, and/or the responseof the transducer/resonant cavity combination.

For a fixed resonant frequency, the matching filter 302 may deliverdifferent amounts of power based on the system resonance(s) inaccordance with the combination of inductor and capacitor values thatare used to form the matching filter network. FIG. 30 illustrates aresponse curve for matching filter configured as a LC network with aninductor value of 1.596 uH and a capacitor value of 3.0 nF. The resonantfrequency of the LC network is 2.3 MHz. Referring to FIG. 30, theresistive impedance is labeled A, the reactive impedance is labeled B,the input real power is labelled C and the acoustic real power into thecavity is labelled D. With regard to the power delivered into thesystem, increasing the capacitor value with the same resonance increasespower into the system. In general, changing the values of the inductorand/or capacitor can influence the resonant frequency of the LC network.Changing the resonant frequency of the LC network changes the frequencyat which optimum power transfer occurs, and can impact the efficiency ofthe transfer. For example, the frequency for optimum power transferrelative to lower or minimum reactance points (label B) of the inputimpedance of the system is influenced by the resonance frequency of theLC network.

The plot in FIG. 30 shows the points on the input real power (C) and theacoustic real power (D) at a reactance minimum. The input real power andacoustic real power are fairly well matched, indicating efficienttransfer of power. If the value of the inductor is changed to 0.8 uH andthe value of the capacitor is changed to 6.0 nF, then the same reactanceminimum produces a greater power transfer with somewhat less efficiency.The power transfer becomes less efficient when the input real power (C)is significantly different (greater) than the acoustic real power (D).In some instances, depending on the inductor and capacitor values, powertransfer can be highly efficient, however, the frequency operating pointmay not be at a minimum reactance point (B). Accordingly, choices can bemade between operating the transducer to obtain highly efficientseparation in the acoustic chamber, implying a minimum reactance point,and obtaining efficient power transfer into the chamber. For a givenmaterial being separated and a given transducer, an LC network can beselected with a resonance frequency to obtain efficient power transferinto the acoustic cavity, improving overall system efficiency.

FIG. 31 is a circuit diagram of one embodiment of the buck filter 318illustrated in FIG. 29. The component values illustrated in FIG. 31 arepresented by way of example, other values and component combinations maybe used to provide the desired filtering.

FIG. 32 is a block diagram illustration of a system 350 for providing atransducer drive signal on the line 352 to an acoustic transducer 354.Referring to FIG. 32, the system 350 controls the transducer 354, whichis coupled to an acoustic chamber 356. The acoustic transducer 354 isdriven by an RF power converter composed of a DC source 358 (e.g., 48volts DC), a DC-DC converter 360 (e.g., a buck converter) and a RF DC-ACinverter 362. Inverter output drive signal on line 364 is input to a lowpass filter 365 (e.g., an LC or LCL matching low pass filter as shown inFIG. 29) and the resultant filtered signal on line 367 is sensed toobtain a voltage sense signal on line 366 and a current sense signal online 368, which are fed back to controller 370. The controller 370provides control signals to the converter 360 and the inverter 362 tocontrol the drive signal on the line 364.

The signal provided by the controller 370 to the converter 360 is apulse width measure, which determines the duty cycle of the switchingsignals in the converter 360. The duty cycle determines the DC level onconverter output signal on line 372, which is applied to the inverter362. For example, the greater the duty cycle, the higher the DC outputon the line 372. The controller 370 provides control signals to theinverter 362 that determine the frequency of operation of the inverter.The control signals provided to the inverter 362 may be switchingsignals, for switching switches (e.g., FETs) in the inverter, an exampleof such switches being shown in FIG. 29. Alternately, or in addition,the controller 370 may provide a control signal to the inverter 362 thatis used to indicate a desired switching frequency, and circuitryinternal to the inverter interprets the control signal and switches theinternal switches in accordance with the interpreted control signal.

The voltage sense signal on the line 366 and the current sense signal onthe line 368 are provided to the controller 370 as feedback signals tocontrol the drive signal on the line 364 provided to the acoustictransducer 354. The controller 370 performs operations and calculationson the feedback signals on the lines 366, 368, for example, to obtain apower measure, P=V*I, or to obtain a phase angle, θ=arctan (X/R).

The controller 370 is provisioned with a control scheme that acceptsprocess settings, such as power output, range of frequency operation, orother user selectable parameters, and provides control signals to theconverter 360 and the inverter 362 based on the process settings and thefeedback values. For example, as described above, the controller cansequence through a number of frequencies in a range of frequencies thatare provided to the inverter 362 to scan through the frequency range anddetermine the characteristics of the transducer 354 or the transducer354 in combination with the acoustic chamber 356, which may be underload. The results of the frequency scan in terms of voltage and currentobtained from the feedback signals on the lines 366, 368 are used toidentify characteristics of the impedance curves for the components orthe system, such as is illustrated in FIG. 33. FIG. 33 is a graphillustrating a frequency response for an acoustic transducer.

The frequency scan can be implemented to occur at set up, and/or atintervals during operation of the illustrated system. Duringsteady-state operation, the frequency scan can be conducted to identifydesired set points for operation, such as power or frequency, based onuser settings and feedback values. The control scheme implemented by thecontroller 370 is thus dynamic, and responds to changing conditions inthe system, such as may be encountered with frequency drift, temperaturechange, load changes and any other system parameter changes. The dynamicnature of the control scheme permits the controller to respond to orcompensate for nonlinearities, such as may be encountered as componentsage or lose tolerance. Accordingly, the control scheme is adaptive andcan accommodate system changes.

Referring still to FIG. 32, some examples of system operation includedriving the acoustic transducer 354 to produce an acoustic standing wave(e.g., a multidimensional acoustic standing wave) in the acousticchamber 356. For example, a 3D acoustic wave may be stimulated bydriving the acoustic transducer 354, which may be implemented as apiezoelectric crystal, sometimes referred to herein as a PZT, near itsanti-resonance frequency. Cavity resonances modulate the impedanceprofile of the PZT as well as affect its resonance modes. Under theinfluence of the 3D acoustic field, suspended particles in the liquidmedium in the acoustic cavity 356 are forced into agglomerated sheetsand then into strings of ‘beads’ of agglomerated material. Once particleconcentrations reach a critical size, gravitational forces take over andthe agglomerated material drops out of the acoustic field and to thebottom of the chamber. The changing concentrations of agglomeratedmaterial as well as the dropping out of that material affects thecavity's resonances which in turn change the acoustic loading on the PZTand its corresponding electrical impedance. The changing dynamics of thecollected material detunes the cavity and PZT reducing the effects ofthe 3D wave in clarifying the medium. Additionally, changes in themedium and cavity temperature also detune the cavity so thatclarification is reduced. To track the resonance changes occurring inthe cavity, a control technique is used to follow changes in the PZT'selectrical characteristics.

A strong 3D acoustic field can be generated by driving the PZT at afrequency where its input impedance is a complex (real and imaginary)quantity. However, cavity dynamics can cause that impedance value tochange significantly in an erratic manner. The changes in impedance aredue, at least in part, to changes in the load applied to the acoustictransducer 354 and/or the acoustic chamber 356. As particles orsecondary fluid is separated from a primary or host fluid, the loadingon the acoustic transducer and/or the acoustic chamber changes, which inturn can influence the impedance of the acoustic transducer and/or theacoustic chamber.

To correct for detuning, the controller 370 calculates the PZT impedancefrom the feedback signals on the lines 366, 368 to change the operatingfrequency to compensate for the detuning. Since frequency changes affectpower delivered to the chamber 356, the controller 370 also determineshow to adjust the output voltage of the (dynamic) converter 360 tomaintain the desired amount of power output from the RF DC-AC inverter362 and into the acoustic transducer 354 and/or the acoustic chamber356.

The converter 360 (e.g., a buck converter) is an electronicallyadjustable DC-DC power supply and is the power source for the inverter362. The inverter 362 converts the DC voltage on the line 372 to ahigh-frequency AC signal on the line 364, which is filtered by filter365 to create a transducer drive signal that drives the PZT 354. Thedynamics in the chamber 356 occur at rates corresponding to frequenciesin the low audio band. Consequently, the converter 360, the controller370, and the DC-AC inverter 362 are capable of working at rates fasterthan the low audio band to permit the controller to track chamberdynamics and keep the system in tune.

The controller 370 can simultaneously change the frequency of the DC-ACinverter 362 and the DC voltage coming out of the buck converter 360 totrack cavity dynamics in real time. The control bandwidth of the systemis a function of the RF bandwidth of the inverter and the cutofffrequency of the filtering system of the buck converter (e.g., seefilter 318 in FIG. 29).

The controller 370 can be implemented as a DSP (digital signalprocessor) control, microcontroller, microcomputer, et cetera or as anapplication specific integrated circuit (ASIC) or a field programmablegate array (FPGA) control, as examples. The controller may beimplemented with multiple channels, to permit parallel processing, forexample to analyze real and/or reactive impedance, voltage, current andpower.

The acoustic dynamics of the cavity 356 affects the electricalcharacteristics of the PZT 354, which affects the voltage and currentdrawn by the PZT. The sensed PZT voltage and current fed back on thelines 366, 368 is processed by the controller 370 to compute thereal-time power consumed by the PZT as well as its instantaneousimpedance (affected by acoustic dynamics). Based on user set points thecontroller 370 adjusts, in real-time, the DC power supplied on the line372 to the inverter 362, and the frequency at which the inverter isoperated to track cavity dynamics and maintain user set points. Thefilter 365 (e.g., an LC or LCL, et cetera) is used to impedance matchthe output impedance of the inverter 362 to increase power transferefficiency.

The controller 370 samples the feedback signals on the lines 366, 368fast enough to detect changes in cavity performance (e.g., via changesin PZT impedance) in real time. For example, the controller 370 maysample the feedback signals on the lines 366, 368 at one hundred millionsamples per second. Signal processing techniques are implemented topermit a wide dynamic range for system operation to accommodate widevariations in cavity dynamics and applications. The DC-DC converter 360can be configured to have a fast response time to follow the signalcommands coming from the controller 370. The inverter 362 can drive awide range of loads that demand varying amounts of real and reactivepower that change over time. The electronics package used to implementthe system illustrated in FIG. 32 may be configured to meet or exceed ULand CE specifications for electromagnetic interference (EMI).

FIG. 34 is a block diagram illustration of an alternative embodimentsystem 380 for providing the transducer drive signal 352 to thetransducer 354. The embodiment of FIG. 34 is substantially the same asthe embodiment in FIG. 32, with a primary difference that the DC-DCconverter 360 and DC-AC inverter 362 of FIG. 32 have been replaced by alinear amplifier 382 (FIG. 32). In addition, the output of controller384 would be an analog sine wave on line 386 that is input to the linearamplifier 382. Referring to FIG. 35, the controller 384 may beimplemented with very-high-speed parallel digital-signal-processingloops using RTL (Register Transfer Level) which is realized in actualdigital electronic circuits inside a field-programmable-gate-array(FPGA). Two high speed digital proportional integral (PI) loops adjustthe frequency of the sine output signal on the line 386. The linearamplifier 382 amplifies the output signal on the line 386 and providesan amplified output signal on line 388, which is filtered using the lowpass filter 365. The resultant voltage and current from the low passfilter 365 are fed back to the controller 384 on lines 366 and 368.Calculations may be performed in series by the controller 384 togenerate control signals to linear amplifier 382. The linear amplifiermay have a variable gain that is set by controller 384. The controller384 (e.g., a FPGA) can be operated, for example, with a clocking signalof 100 MHz. In a real time system, the clock speed (e.g., sample rates,control loop update rates, et cetera) may be fast enough to properlymonitor and adapt to conditions of the PZT 354 and/or the chamber 356.In addition, the structure of the FPGA permits each gate component tohave a propagation delay commensurate with the clocking speed. Thepropagation delay for each gate component can be less than one cycle, orfor example 10 ns with a clocking speed of 100 MHz.

Referring to FIG. 35, a diagram illustrates parallel and sequentialoperations for calculating control signals. The controller 384 may beconfigured to calculate the following parameters.

VRMS=sqrt(V1² +V2² + . . . +Vn ²)

IRMS=sqrt(I1² +I2² + . . . +In ²)

Real Power(P=V-Inst.×I-Inst Integrated over N Cycles)

Apparent Power(S=VRMS×IRMS)

The controller 384 may be configured to calculate reactive power andbipolar phase angle by decomposing sensed voltage and current intoin-phase and quadrature-phase components. FIG. 36 illustrates thein-phase and quadrature-phase demodulation of the voltage and current toobtain a four-quadrant phase, reactive power and reactance. Thecalculations for reactive power and phase angle can be simplified usingthe in-phase and quadrature-phase components.

VPhase Angle=Arctan(QV/IV)

IPhase Angle=Arctan(QI/II)

Phase Angle=VPhase−IPhase

Reactive Power=(Q=Apparent Power×Sine(Phase Angle)

The controller 384 may implement a control scheme that begins with afrequency sweep to determine system performance parameters at discretefrequencies within the frequency sweep range. The control scheme mayaccept inputs of a start frequency, a frequency step size and number ofsteps, which defines the frequency sweep range. The controller providescontrol signals to the linear amplifier 382 to modulate the frequencyapplied to the PZT 354, and the voltage and current of the PZT are fedback to the controller on lines 366, 368. The control scheme of thecontroller 384 may repeat the frequency sweep a number of times todetermine the system characteristics, for example, reactance, with arelatively high level of assurance.

A number of reactance minimums can be identified as a result of analysisof the data obtained in the frequency sweep. The control technique canbe provided with an input that specifies a certain frequency range wherea desired reactance minimum is located, as well as being provided with aresistance slope (+/−) that can be used for tracking a desired point ofoperation based on resistance tracking that corresponds to a desiredminimum reactance. The resistance slope may be constant near the minimumreactance, which may provide a useful parameter for use with a trackingtechnique. By tracking resistance at a desired frequency, a robustcontrol can be attained for operating at a minimum reactance point.

The control technique may take the derivative of theresistance/reactance values to locate zero slope derivatives, which areindicative of maximums and minimums. Aproportional-integral-differential (PID) controller loop may be used totrack the resistance to obtain a frequency setpoint at which a desiredminimum reactance occurs. In some implementations, the control may be aproportional-integral (PI) loop. With the FPGA operating at 100 MHz,adjustments or frequency corrections can be made every 10 ns tocompensate for changes in the tracked resistance. This type of controlcan be very accurate and implemented in real-time to manage control ofthe PZT in the presence of a number of changing variables, includingreactance, load and temperature, for examples. The control technique canbe provided with an error limit for the frequency of the reactanceminimum or frequency setpoint, to permit the control to adjust theoutput to linear amplifier 382 to maintain the frequency within theerror limit.

A fluid mixture, such as a mixture of fluid and particulates, may beflowed through the acoustic chamber to be separated. The fluid mixtureflow may be provided via a fluid pump, which may impose perturbations onthe fluid, as well as the PZT and chamber. The perturbations can createa significant fluctuation in sensed voltage and current amplitudes,indicating that the effective impedance of the chamber fluctuates withpump perturbations. However, owing to the speed of the controltechnique, the fluctuations can be almost completely canceled out by thecontrol method. For example, the perturbations can be identified in thefeedback data from the PZT and can be compensated for in the controloutput from the controller. The feedback data, for example the sensedvoltage and current, may be used to track the overall acoustic chamberpressure. As the characteristics of the transducer and/or acousticchamber change over time and with various environmental parameters, suchas pressure or temperature, the changes can be sensed and the controltechnique can compensate for the changes to continue to operate thetransducer and acoustic chamber at a desired setpoint. Thus, a desiredsetpoint for operation can be maintained with very high accuracy andprecision, which can lead to optimized efficiency for operation of thesystem.

The FPGA may be implemented as a standalone module and maybe coupledwith a class-D driver. Each module may be provided with a hardcodedaddress so that it can be identified when connected to a system. Themodule can be configured to be hot-swappable, so that continuousoperation of the system is permitted. The module may be calibrated to aparticular system and a transducer, or may be configured to perform acalibration at particular points, such as upon initialization. Themodule may include long-term memory, such as an EEPROM, to permitstorage of time in operation, health, error logs and other informationassociated with operation of the module. The module is configured toaccept updates, so that new control techniques can be implemented withthe same equipment, for example.

FIG. 37 is a simplified circuit illustration of an RF power supply 396that includes a voltage source 398 what provides a signal on a line 400to an LC matching filter 402, which provides a transducer drive signalon line 404 to ultrasonic transducer 406. FIG. 38 is a simplifiedcircuit illustration of an RF power supply 408 substantially the same asthe power supply illustrated in FIG. 36, with the exception of an LCLmatching filter 410 rather than the LC filter 402 illustrated in FIG.36.

FIG. 39 is a circuit diagram of an RF power supply 412 that provides adrive signal on line 414 to an LCL low pass filter 416, which provides atransducer drive signal on line 418 to an ultrasonic transducer 420. Acontroller (e.g., see controller 370 in FIG. 32) provides complementarycontrol signals to first FET switch 422 and second FET switch 424 of aDC-AC inverter 426, and the resultant AC drive signal is provided on theline 414. The frequency of the complementary controls signals applied tothe switches 422, 424 is controlled by the controller in order to setthe frequency of the signal on the line 414. The signal on the line 414is low pass filtered to attenuate high frequency components, and ideallyprovide a sine wave on line 418. An example of a dynamic model of theultrasonic transducer 420 is also illustrated in FIG. 39.

FIG. 40 is a simplified circuit illustration of an LCL filter circuit430 with a tap that provides a current sense signal I_(RF) and a nodethat provides a voltage sense signal V_(RF). The signals I_(RF) andV_(RF) are fed back to a controller 431 (e.g., a DSP) to control atransducer drive signal (e.g., frequency and power) on a line 432applied to transducer 434.

FIG. 41 is a schematic illustration of an embodiment of a power supplythat includes an inverter 440 that receives from a controller (notshown) a switching signal on line 442 and a complement thereof on line444, which a used to drive first and second FETs 446, 448. The resultantAC signal on line 450 is input to a LCL filter 452, and the resultantfiltered signal is output to drive the transducer. The filter 452 actsas a current source to drive the transducer.

It is contemplated that drivers and filters disclosed herein may be usedto generate planar waves.

The present disclosure has been described with reference to exemplaryembodiments. Modifications and alterations may occur to others uponreading and understanding the preceding detailed description. It isintended that the present disclosure be construed as including all suchmodifications and alterations insofar as they come within the scope ofthe appended claims or the equivalents thereof.

What is claimed is:
 1. An apparatus for driving a variable impedanceload, comprising: an electronic driver that includes an inverterconfigured to produce an RF output; a control circuit coupled to thevariable impedance load and to the driver and configured to control thedriver to provide a drive signal for the load; and the control circuitbeing configured to receive feedback signals from the load and controlthe driver based on a reactance value obtained from the feedbacksignals.
 2. The apparatus of claim 1, where the control circuitcomprises a digital signal processor.
 3. The apparatus of claim 1,further comprising a compensation circuit between the driver and theload.
 4. The apparatus of claim 3, wherein the compensation circuitfurther comprises an inductive component and a capacitive component. 5.The apparatus of claim 1, further comprising a DC-DC converter coupledto the control circuit and the inverter.
 6. An apparatus for driving anultrasonic transducer at radio frequencies (RF), comprising: anelectronic driver coupled to the ultrasonic transducer for exciting theultrasonic transducer; and a DC-DC converter and an inverter included inthe driver.
 7. The apparatus of claim 6, further comprising a conversioncircuit between the DC-DC converter and the inverter.
 8. The apparatusof claim 7, wherein the conversion circuit is configured to convert aPWM signal to a DC signal.
 9. The apparatus of claim 6, furthercomprising a scaling circuit that is configured to convert a voltagedrive signal to a current drive signal.
 10. The apparatus of claim 9,wherein the scaling circuit consists of passive circuit components. 11.The apparatus of claim 6, further comprising a controller coupled to theultrasonic transducer and to the driver, the controller configured toreceive feedback signals from the ultrasonic transducer and to controlthe driver in accordance with the feedback signals.
 12. A method fordriving a variable impedance load, comprising: controlling an electronicdriver that includes an inverter to produce an RF output to the load;determining a control for the electronic driver based on feedbacksignals from the load; and providing the control to the electronicdriver to produce the RF output to the load.
 13. The method of claim 12,further comprising using a digital signal processor for determining thecontrol.
 14. The method of claim 12, further comprising compensating theRF output to the load.
 15. The method of claim 12, further comprisingconverting the RF output from a voltage drive signal to a current drivesignal.
 16. The method of claim 12, wherein the electronic driverfurther comprises a DC-DC converter; and driving the DC-DC converter toproduce a power output to the inverter.